The emergence of the Virasoro and $w_infty$ algebras through the renormalized higher powers of quantum white noise

We introduce a new renormalization for the powers of the Dirac delta function. We show that this new renormalization leads to a second quantized version of the Virasoro sector $w_{\infty}$ of the extended conformal algebra with infinite symmetries $W_{\infty}$ of Conformal Field Theory ( \cite{4a}-\cite{4d}, \cite{ketov}, \cite{7}, \cite{8}). In particular we construct a white noise (boson) representation of the $w_{\infty}$ generators and commutation relations and of their second quantization.